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"Online" as an adjective is practically meaningless these days. Can you elaborate/focus on what specifically you're trying to learn with this question? Are you talking about language courses (1-on-1 or group) via Skype? Are you talking about entirely individualized instruction (Duolingo)? Are you talking about using online resources (dictionaries, grammar books)? In the western world, almost everything is done, at least in part, "on line" these days.
– FlimzyApr 6 '16 at 8:44

I think this could be reopened because even if the question sounds broad, two succinct and valuable answers have been posted. It it possible to answer this question without going into great detail.
– SuperBiasedManApr 6 '16 at 9:53

It feels a bit like saying "What is the efficiency of (book/telephone/television/radio) based learning"?
– Andrew GrimmApr 7 '16 at 8:35

2 Answers
2

Not restricting it to Duolingo et al. specifically the name of this research field is CALL (computer assisted language learning). There's at least two major journals devoted to this in all of its aspects:

ReCALL - which is the journal of the Journal of the European Association for Computer Assisted Language Learning

Here is one such study, but it appears to be at least commissioned by Duolingo itself even if it was carried out independently. Here is an independent critique written by Michael Schmitz, an online German educator which compares Duolingo to his more traditional classroom courses.

In general I am of the opinion that there are not enough studies to make a definitive conclusion about overall effectiveness, mostly because the choice to use Duolingo to learn may largely depend on how one prefers to learn the language. Duolingo can be used much more casually than a classroom course so it is somewhat difficult to compare them in that respect. However, you should be able to find enough information to decide how you would prefer to learn (and if you're still not sure, you can always try out Duolingo because it's free).

Note: Duolingo even has a research page that you can visit to learn more and which might be updated with related studies in the future.

The fact that a particular company or organization sanctioned or commissioned the research doesn't invalidate them. In many cases, it leads to a better understanding of why that program is structured a certain way and what further development will be done. I am glad that you included it in your answer.
– callyalaterApr 7 '16 at 15:41